Manifestly Gauge-Invariant Cosmological Perturbation Theory from Full Loop Quantum Gravity

Abstract

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the new cosmological perturbation theory of LQG, and various power spectrums are studied for scalar mode and tensor mode perturbations. Comparing these power spectrums with predictions from the classical theory demonstrate corrections in the ultra-long wavelength regime. These corrections are results from the lattice discretization in LQG. In addition, tensor mode perturbations at late time demonstrate the emergence of spin-2 gravitons as low energy excitations from LQG. The graviton has a modified dispersion relation and reduces to the standard graviton in the long wavelength limit.

26 pages, 16 figures. ILQGS talk: http://relativity.phys.lsu.edu/ilqgs/han041420.mp4. Mathematica files can be downloaded from https://github.com/LQG-Florida-Atlantic-University/cos_pert

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• Loop Quantum Gravity on Dynamical Lattice and Improved Cosmological Effective Dynamics with Inflaton
• Loop quantum cosmology: relation between theory and observations
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Scalar Quasi-Normal Modes of a Loop Quantum Black Hole
• Friedmann equations and cosmic bounce in a modified cosmological scenario
• The Semiclassical limit of $SU(3)$ Gauge Field Coherent States: Peakedness and Overlap Functions